graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

, the Krackhardt kite graph is a

simple graph In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called '' v ...

with ten nodes. The graph is named after

David Krackhardt David Krackhardt is Professor of Organizations at Heinz College and the Tepper School of Business, with courtesy appointments in the Department of Social and Decision Sciences (Dietrich College of Humanities and Social Sciences) and the Machine L ...

, a researcher of social network theory. Krackhardt introduced the graph in 1990 to distinguish different concepts of

centrality In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, k ...

. It has the property that the vertex with maximum

degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathemati ...

(labeled 3 in the figure, with degree 6), the vertex with maximum

betweenness centrality In graph theory, betweenness centrality (or "betweeness centrality") is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph, there exists at least one shortest path between the vertices suc ...

(labeled 7), and the two vertices with maximum

closeness centrality In a connected graph, closeness centrality (or closeness) of a node is a measure of centrality in a network, calculated as the reciprocal of the sum of the length of the shortest paths between the node and all other nodes in the graph. Thus, the ...

(labeled 5 and 6) are all different from each other.

References

{{Combin-stub Individual graphs